Bilinear control to trajectories of 1D degenerate parabolic equations in moving domains

TL;DR

This paper investigates the local controllability of 1D degenerate parabolic equations in moving domains, focusing on steering the system to a positive trajectory using bilinear control methods.

Contribution

It introduces a novel approach combining local inversion techniques with specific estimates to achieve controllability in degenerate, time-evolving domains.

Findings

Achieved local controllability to positive trajectories in degenerate parabolic equations.

Developed estimates tailored for equations in moving domains.

Extended control methods to a class of semilinear degenerate PDEs.

Abstract

In this paper, we are concerned with local controllability properties of degenerate parabolic equations in bounded domains that evolve in time. More precisely, we deal with the exact controllability to a positive trajectory of a one-dimensional semilinear degenerate equation governed via the coefficient of the reaction term. We apply a well-known local inversion method combined with some appropriate specific estimates.